C/D y1[n] x1(t) x2(t) T=12kHzC/DC H(z)x1(t) x2(t) T1=12KHzC/D AT2=6KHzBy2[n]2 2 x[n] y1[n] H1(ejω)H2(ejω) x[n]Homework Set #3: Continuous to Discrete Time Translation1.The signal xc(t) = 2cos(200πt) is sampled with sampling periods, (a)T = 1/300; (b)T = 1/150; (c)T = 1/100; (d)T = 1/50 seconds, what are the resulting sampling sequences, x[n]? 2.The signal xc(t) = sin(200πt) + cos(50πt) is sampled with sampling periods, (a)T = 1/500; (b)T = 1/200; (c)T = 1/100; (d)T = 1/50 seconds, what are the resulting sampling sequences, x[n]? 3.Consider the system show below. For each of the following input signal x[n], indicate whether the output xr[n] = x[n]: (a)x[n] = cos(πn/5); (b)x[n] = cos(πn/4); (c)x[n] = cos(πn/3); (d)x[n] = ncos(πn/2);(e)x[n] = sin(πn) 4.Consider audio signal sampling and reconstruction, we plan to design 6-time oversampling system (by using ideal digital low pass filter) to reduce the burden of the design of analog filters. The original signal sampling and reconstruction systems are shown as: (a) Specify the original frequency responses of Ha(j
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